41117 ÷ 7 = 5873 R6
Alright, let's work through the division of 41117 by 7 step by step.

Step 1:
7 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 4 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 7

Step 2:
7 goes into 41 5 times with a remainder of 6.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 35 from 41 to get 6.
Bring next digit (1) of the dividend behind the 6 and repeat the process: 61 / 7

Step 3:
7 goes into 61 8 times with a remainder of 5.
Write down 8 as next digit of of the result. 
Result so far: 58
Subtract 56 from 61 to get 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 7

Step 4:
7 goes into 51 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 587
Subtract 49 from 51 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 7

Step 5:
7 goes into 27 3 times with a remainder of 6.
Write down 3 as next digit of of the result. 
Result so far: 5873
Subtract 21 from 27 to get 6.

The final result is 5873 with a remainder of 6.